Like nrhareiner said, it all depends on what you're doing.
In a horsemanship class where you're being judged on your position and how well you communicate with your horse. You'll be sitting very much like the first pic you showed where ideally your shoulder hip and heel will be in alignment. Heels down eyes forward, etc. Although in my experience, you have a deeper seat in western than you would hunt seat, so you would sit on your pockets more so than rolling your hips forward. I don't know enough about reining to explain the seat right, so I'll leave that to someone else.